Mathematics - ICT - MedicineMathematics - ICT - Medicine

ProjectsProjects

External ProjectsMathematics / Physics / Statistics / ICT

Internal ProjectsSimReal+ (SimReal + SimVideo)

SimReal+Interactice Learning Tool in Mathematics / Physics / Statistics / Computer Science Video Lesson / Live Streaming / Video Simulation / Interactive Simulation / Exercise / Applicaction

Video LessonStreamingVideo SimulationInteractive SimulationExerciseApplication

MathematicsParabel

SimReal+ - ResearchSimReal+ - Research

Brekke : LICE conferenceLondon International Conferenceon Education

Brekke/Hogstad : JournalNew teaching methodsUsing computer technologyin physics and mathematics

Elira Curri : Master Thesis (UiA, Albania)Ninni Marie Hogstad : Master Thesis (UiA)

Comments / ResultsComments / Results

- A great supplement, and very good academic contents

- A great way to repeat past lectures

- I wish this could be used in all my courses

- Enables me to get a better understanding of the subject

- Extremely impressive that you have spent all this time to create such a fantastic tool.

Survey Exam - Physics

Comments from the students

Projects - SimReal+Projects - SimReal+

External ProjectsMathematics / Physics / Statistics / ICT

Internal ProjectsSimReal+ (SimReal + SimVideo)

The Norwegian Radiumhospital in OsloLinear AcceleratorThe Norwegian Radiumhospital in OsloLinear Accelerator

- Control of the Linear Accelerator- Databases (patient/employee/activity)- Computations of patient positions

PatientDatabase

Computer

Linear Accelerator

MRIMagnetic Resonance ImagingMRIMagnetic Resonance Imaging

Transformation Home Car RepairHospital

Transformation TheoryTransformation Theory

TransformasjonTransformasjonf(x)f(x) F(u)F(u)Room 1 Room 2

f(x) = T-1(F(u))f(x) = T-1(F(u))

F(u) = T[f(x)] F(u) = T[f(x)]

N=2

N=10

Fourier TransformationFourier SerieFourier TransformationFourier Serie

1

1

0

])12sin[(12

14

2sin

2cos

2)(

n

nnn

xnn

T

xnb

T

xna

axf

N

n

xnn

xf1

])12sin[(12

14)(

Definition of The Continuous Wavelet Transform CWTDefinition of The Continuous Wavelet Transform CWT

0 , )(, 2 aRbaRLf

The continuous-time wavelet transform (CWT)of f(x) with respect to a wavelet (x):

dxxfxfbafWbaW baba )()(),]([),( ,,

a

bxaxba

2/1, || )(

dadbxbaWaC

xf ba )(),(11

)( ,2

][ fW ),] ([ bafW

)( xf

)( xL2(R ))(0,1 x )(0,2 x )(1,2 x

1σ

2a 1a yx

The Norwegian RadiumhospitalMammographyMicro-calcificationsWavelet Transformation - Mexican Hat

The Norwegian RadiumhospitalMammographyMicro-calcificationsWavelet Transformation - Mexican Hat

2

2

2σ

x2

2π1 e

σ

x2Ψ (x)

brPbrT

a

T

y

brPbr

2

1

a2 π

1b,a

e2)r(Ψx

y

xr

y

x

b

bb

y

x

a

aa

cosθsin θ

sin θcosθR

2

y

2x

a

10

0a

1

A A RRP T

ECG

MammographySeismic

The Norwegian RadiumhospitalMammographyMicro-calcifications

The Norwegian RadiumhospitalMammographyMicro-calcifications

DiameterRelative contrastNumber of microcalcifications

Mathematical tranformationof the mammography imaging

Mammographyphantom Phantom information

Transformed image

UltrasoundUltrasound

Ultrasound Image - Edge detectionSINTEF – Unimed – Ultrasound - TrondheimUltrasound Image - Edge detectionSINTEF – Unimed – Ultrasound - Trondheim

- Ultrasound Images- Egde Detection

- Noise Removal- Egde Sharpening- Edge Detection

Prosthesis

OsteroporosisOsteroporosis

External part External part

[f]Wa

1ψ2

E/I bone edge E/I bone edge

a

bxaxba 2/1

, || )(

xex x

2ln

2cos)(

2

Morlet

HeartCirculationHeartCirculation

Mathematical ApplicationsMathematical Applications

PresentationPresentation

Per Henrik Hogstad

University of Agder

- Mathematics- Statistics- Physics (Main subject: Theoretical Nuclear Physics)- Computer Science

- Programming / Objectorienting- Algorithms and Datastructures- Databases- Digital Image Processing- Supervisor Master Thesis

-Research- Mathematics of Wavelets + Computer Application Wavelets / Medicine- SimReal+ (SimReal + SimVideo)

SimReal+Calculator - Graph - Function Analysis - Built in Function

SimReal+Calculator - Regression Analysis

Transformation TheoryIntegral TransformationWavelet - Laplace - Fourier

Transformation TheoryIntegral TransformationWavelet - Laplace - Fourier

f(…)f(…) F(…)F(…)

Fourier

jsdttfestfL s t

)())](([

Wavelet

Laplace

d xxfexfFuF u xj )()()( 2

d xxfxfbafWbaW baba )()(),] ([),( ,,

Wavelet TransformMammography - VideoWavelet TransformMammography - Video

PETEmission of PositronsPETEmission of Positrons

PET radiotracer (18F fluorodeoxyglucose (FDG))+ radioactive fluorine.Natural decay includes emmission of positronsthat reach with electrons (annihilaation) in the bodyproduces energy in the form of a pair of photons.The PET skanner, which is able to detect these photons,creates three-dimensional images that show how the FDG is distributed in the area of the body.

Areas where a large amount of FDG accumulates,called ’hot spots’ because they appear more intensethan surrounding tissue, indicate that a high level of chemical activity or metabolism is occuring there.

Calculator in MedicineSafety CalculatorCalculator in MedicineSafety Calculator

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